Russian authorities should annul the parliamentary vote results and hold a new election, the ex-Soviet leader Mikhail Gorbachev has urged, as popular indignation grows over alleged election fraud.

Thousands of Russians have rallied in Moscow and St Petersburg in the past two days, facing off against tens of thousands of police and interior ministry troops. Hundreds of protesters have been detained in both cities.

Gorbachev told the Interfax news agency that authorities must hold a fresh election or deal with a rising tide of discontent.

Vladimir Putin's United Russia party won less than 50% of Sunday's vote, a steep fall from its earlier two-thirds majority, according to preliminary results. But opposition parties and international observers said the vote was marred by vote-rigging, including alleged ballot-box stuffing and false voter rolls.

"More and more people are starting to believe that the election results are not fair," he told Interfax. "I believe that ignoring public opinion discredits the authorities and destabilises the situation."

Gorbachev added that authorities "must admit that there have been numerous falsifications and ballot stuffing".

Sunday's parliamentary vote suggested Russians are tiring of Putin and his United Russia party, which has dominated all other political forces in the country for a dozen years and earned a reputation for corruption.

Putin, meanwhile, officially registered on Wednesday to run for the presidency in March, but the unusually sustained protests of the past two days suggested his drive to retake the job he held from 2000-2008 may not go as smoothly as he had expected.

More opposition rallies were expected, along with another new pro-Putin gathering in central Moscow.